A Robust Approach to Detecting Non-equivalent Quantum Circuits Using Specially Designed Stimuli

As several compilation and optimization techniques have been proposed, equivalence checking for quantum circuits has become essential in design flows. The state-of-the-art to this problem ob-served that even small errors substantially affect the entire quantum system. As a result, it exploited random simulations to prove the non-equivalence of two quantum circuits. However, when errors occurred close to outputs, it was hard for the work to prove the non-equivalence of some non-equivalent quantum circuits under a limited number of simulations. In this work, we propose a novel simulation-based approach using a set of specially designed stimuli. The simulation runs of the proposed approach is linear rather than exponential to the number of quantum bits of a circuit. According to the experimental results, the success rate of our approach is 100% (100%) under a simulation run (execution time) constraint for a set of benchmarks, while that of the state-of-the-art is only 69% (74%) on average. Our approach also achieves a speedup of 26 on average.